scholarly journals Optimal learning rates for least squares regularized regression with unbounded sampling

2011 ◽  
Vol 27 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Cheng Wang ◽  
Ding-Xuan Zhou
Keyword(s):  
Least Squares ◽  
Regularized Regression ◽  
Optimal Learning ◽  
Learning Rates

scholarly journals Approximation by multivariate max-product Kantorovich-type operators and learning rates of least-squares regularized regression

2020 ◽  
Vol 19 (8) ◽  
pp. 4213-4225 ◽  
Author(s):  
Lucian Coroianu ◽  
◽  
Danilo Costarelli ◽  
Sorin G. Gal ◽  
Gianluca Vinti ◽  
...  
Keyword(s):  
Least Squares ◽  
Regularized Regression ◽  
Learning Rates

Learning rates for regularized least squares ranking algorithm

2017 ◽  
Vol 15 (06) ◽  
pp. 815-836 ◽  
Author(s):  
Yulong Zhao ◽  
Jun Fan ◽  
Lei Shi
Keyword(s):  
Least Squares ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Ranking Algorithm ◽  
Generalization Error ◽  
Ranking Problem ◽  
Regularized Least Squares ◽  
U Statistics ◽  
Learning Rates ◽  
Error Decomposition

The ranking problem aims at learning real-valued functions to order instances, which has attracted great interest in statistical learning theory. In this paper, we consider the regularized least squares ranking algorithm within the framework of reproducing kernel Hilbert space. In particular, we focus on analysis of the generalization error for this ranking algorithm, and improve the existing learning rates by virtue of an error decomposition technique from regression and Hoeffding’s decomposition for U-statistics.

scholarly journals Learning rates for the risk of kernel-based quantile regression estimators in additive models

2016 ◽  
Vol 14 (03) ◽  
pp. 449-477 ◽  
Author(s):  
Andreas Christmann ◽  
Ding-Xuan Zhou
Keyword(s):  
Hilbert Space ◽  
Quantile Regression ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Gaussian Function ◽  
Additive Model ◽  
Additive Models ◽  
Gaussian Kernel ◽  
Optimal Learning ◽  
Learning Rates

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel-based methods for additive models. These learning rates compare favorably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel-based quantile regression using the Gaussian radial basis function kernel, provided the assumption of an additive model is valid. Additionally, a concrete example is presented to show that a Gaussian function depending only on one variable lies in a reproducing kernel Hilbert space generated by an additive Gaussian kernel, but does not belong to the reproducing kernel Hilbert space generated by the multivariate Gaussian kernel of the same variance.

scholarly journals Optimal learning rates for unbiased perception

2010 ◽  
Vol 3 (9) ◽  
pp. 175-175 ◽  
Author(s):  
B. T Backus
Keyword(s):  
Optimal Learning ◽  
Learning Rates
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